Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated

Bioinspired ligand designs for cobalt, iron and manganese complexes : understanding mono-iron hydrogenase (Hmd)

Mono-iron hydrogenase is one of three types of hydrogenases, catalyzing reversible hydride transfer to the substrate (methenyl-H₄MPT⁺) by heterolytically cleaving molecular hydrogen into a proton and a hydride. The key features of the enzyme’s active site include a pyridone moiety, an acyl unit and facial ligation of C [superscript acyl] N [superscript pyridone] S [superscript Cys] donors. Each feature was independently incorporated into a selected ligand system (Schiff-base N4, pincer and thianthrene scaffold, respectively), in efforts to i) develop possible bioinspired catalysts for H₂ activation using earth abundant metals (iron, cobalt, manganese) and ii) make synthetic models of the enzyme active site for deeper understanding of the architecture of the active site and catalytic mechanism. Synthetic routes for making pyridone-based Schiff-base N4 and NNS type ligands were explored: although not isolated, the ligands were spectroscopically detected. On the other hand, the simpler version—pyridine-based Schiff-base N4 ligands—afforded dinuclear cobalt complexes upon metalations with cobalt(II) precursors. Depending on the length of the diamine-linker as well as the substituents on the pyridine rings, either spontaneous O₂ activation or B–F activation was observed, yielding μ-peroxo dicobalt(III) complexes or μ-fluoride bridged dicobalt(II) complexes, respectively. In particular, two μ-fluoride bridged dicobalt complexes showed antiferromagnetic coupling between the two cobalt(II) centers. From the pincer ligands featuring the unique acyl moiety within C [superscript acyl] N [superscript pyridine] S [superscript thioehter] and C [superscript acyl] N [superscript pyridine] P [superscript Ph2] donor set, the (expected) meridional and an (unexpected) facial iron-acyl complexes were isolated, respectively. Upon deprotonation (pyridine→pyridinate de-aromatization), both complexes showed reactivity towards H₂ activation; no evidence for hydride-transfer was observed. For the facial ligation, thianthrene-scaffolded manganese system was examined as a more flexible version of the anthracene-scaffolded systems. Preliminary results of the kinetic studies support the correlation between the flexibility of the scaffold and the reactivity of the metal complex, without greatly altering the electronic environment of the metal center.Chemistr

Internal wave generating turbulent mixing in the Canada Basin

The Tenth Symposium on Polar Science/Ordinary sessions: [OM] Polar Meteorology and Glaciology, Thu. 5 Dec. / 2F Auditorium , National Institute of Polar Researc

Dance with Me Tonight

Both music and poetry are used to describe experiences and communicate feelings. They express feelings or situations that are meaningful to the artists and speak to every level of emotion. I believe all music has expressive power, some musical works reveal this more than others, but all music carries meaning, with each work uniquely expressing that meaning. Dance With Me Tonight, a poem by Kristi Day, year unknown, has 12 stanzas. The work is mostly used in weddings and anniversaries. As much as I understood of the author\u27s work, the piece begins in a minor mood setting to demonstrate the author\u27s dearest wish to dance with her lover. The music continues and the moods change as the author\u27s inner mind and struggles change from desperate to hopeful. The music and lyrics together represent the inner voice of the narrator. The tension builds until the final climax in the middle part, and then it slowly releases, changing the mood with a switch to a major key. The music gives both oboe and piano the same significant value as the soprano voic